Legislation was defeated by just six votes in the Church's parliamentary body, the General Synod 2 weeks ago.
Despite receiving the majority of Synod votes, the legislation fell because it could not secure the required two-thirds majority from the laity.
The Church was forced to address the issue in Parliament in response to an urgent question tabled by Labour MP Diana Johnson.
She told MPs that the Church was being "held to ransom by a few narrow minds".
"There should be no stained-glass ceiling for women in our church," she said. "The Church of England now stands to be left behind by the society it seeks to serve, looking outdated, irrelevant, and frankly eccentric by this decision."
Conservative MP and Second Churches Estates Commissioner, Sir Tony Baldry, said he shared the frustration of MPs but highlighted that the legislation had received a yes vote from 94% of bishops and 77% of the House of Clergy, and that even among the laity, 64% had voted in favour.
He admitted: "It is impossible for me to explain to parliamentary colleagues how a measure that has had the support of 42 out of the 44 dioceses failed to pass in General Synod."
He added, however, that legislation on women bishops could be re-considered by General Synod before 2015.
"This is not an issue that can in any way be parked for the next couple of years or so, while we await another round of Synod elections," he said.
He continued: "It is perfectly possible for a different and amended measure to consecrate women bishops to be considered by General Synod."
The outcome of Tuesday's vote was also challenged by Tory backbencher Eleanor Laing, who said that the Church of England's position as the established church "must be called into question".
Sir Tony responded by saying she had made a "perfectly good point".
"What has happened as a consequence of the decision by general synod is the Church of England no longer looks like a national church, it simply looks like a sect like any other sect," he said. "If the Church of England wants to be a national church, then it has to reflect the values of the nation."
Prime Minister David Cameron responded to the vote earlier in the week by saying that the Church needed a "sharp prod" and to "get with the programme".
Sir Tony said he would be arranging a meeting between concerned MPs and the Archbishop-designate, Bishop Justin Welby.